Answered

IDNLearn.com provides a seamless experience for finding the answers you need. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.

A vector has the components Ax=22 m and Ay=13 m. What is the magnitude of thisvector? What angle does this vector make with the positive x axis?

Sagot :

Answer:

Magnitude = 25.55 m

Angle = 30.58 degrees

Explanation:

If the vector has the components Ax = 22 and Ay = 13, we can represent the vector as:

Therefore, the magnitude of this vector is the magnitude of the red vector. It means that we can calculate its length using the Pythagorean theorem where 22 and 13 are the legs, so:

[tex]\sqrt[]{Ax^2+Ay^2}=\sqrt[]{22^2+13^2}=\sqrt[]{484+169}=\sqrt[]{653}=25.55\text{ m}[/tex]

Then, we can find the angle using the trigonometric function tangent, so:

[tex]\begin{gathered} \tan \theta=\frac{Ay}{Ax} \\ \tan \theta=\frac{13}{22} \\ \tan \theta=0.5909 \\ \theta=\tan ^{-1}(0.5909) \\ \theta=30.58 \end{gathered}[/tex]

So, the answers are:

Magnitude = 25.55 m

Angle = 30.58 degrees

View image CailebV517258
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.